Modified FBA in a production network

Abstract

A method for matching production of FBA metabolism to supply and demand within a larger production network is described herein. An objective function of FBA metabolism is modified to include an upstream supply generated in upstream sub-units, as well as a downstream demand generated within downstream sub-units in the production network. FBA metabolism and the upstream and downstream sub-units are iteratively solved with updated initial conditions, producing a time series solution to the production network.

What is claimed is: 
     
       1. A method for simulating an outcome of a cell process of at least one cell in a production network, the method comprising:
 receiving an initial state dataset based on initial net demand for a plurality of molecules in a plurality of sub-units representing production and consumption of molecules external to a flux balance analysis (FBA) system, wherein multiple sub-units of the plurality of sub-units represent transcription, translation, cellular communication, cellular respiration, cellular reproduction, or cellular transport; 
 calculating an initial solution flux dataset by evaluating the FBA system based on a stoichiometric matrix and an objective function, the objective function based on a difference between a first target value for each molecule of the plurality of molecules and a first proportional flux contribution of each molecule of the plurality of molecules, wherein the first target value is included in a set of initial target values calculated based on the initial state dataset; 
 receiving a subsequent net demand for the plurality of molecules from initial solutions to the plurality of sub-units; 
 calculating a subsequent state dataset for the plurality of molecules in the plurality of sub-units based on the initial state dataset, the initial solution flux dataset, and the subsequent net demand; 
 updating the objective function, the updated objective function based on a difference between a second target value for each molecule of the plurality of molecules and a second proportional flux contribution of each molecule of the plurality of molecules, wherein the second target value is included in a set of subsequent target values calculated based on the subsequent state dataset; 
 calculating a subsequent solution flux dataset by evaluating the FBA system with the updated objective function; and 
 determining the outcome of the cell process of the at least one cell, the determining includes calculating a difference between the subsequent solution flux dataset and the initial solution flux dataset, wherein the outcome of the cell process corresponds to an estimation of a growth rate of the at least one cell, and wherein an accuracy of the updated objective function is determined based on a comparison of the estimation of the growth rate of the at least one cell to an actual growth rate of the at least one cell. 
 
     
     
       2. The method of  claim 1 , wherein:
 the initial state dataset includes a set of initial molecule concentrations of the plurality of molecules; and 
 the initial net demand for the plurality of molecules comprises: 
 an initial rate of supply in a first sub-unit representing production upstream from metabolism; and 
 an initial rate of demand in a second sub-unit representing consumption downstream from metabolism. 
 
     
     
       3. The method of  claim 2 , wherein the set of initial molecule concentrations of the plurality of molecules comprises:
 a total concentration of each of the plurality of molecules in the plurality of sub-units; and 
 a cushion concentration representing a reserve concentration of each of the plurality of molecules. 
 
     
     
       4. The method of  claim 1 , wherein the initial state dataset further includes:
 a set of intrinsic rate parameters for each of the plurality of molecules, wherein the set of intrinsic rate parameters represents a biological ability of the cell to adjust the subsequent solution flux dataset to the subsequent net demand for the plurality of molecules. 
 
     
     
       5. The method of  claim 4 , wherein the set of intrinsic rate parameters for each of the plurality of molecules includes at least one of: a proportional rate limit, an integral rate limit, and a derivative rate limit. 
     
     
       6. The method of  claim 1 , wherein calculating the initial solution flux dataset by evaluating the FBA system based on the stoichiometric matrix and the objective function limited by the initial state dataset further comprises:
 maximizing the objective function limited by the initial state dataset within a constraint of the stoichiometric matrix to determine a maximum growth rate. 
 
     
     
       7. The method of  claim 1 , wherein the initial solution flux dataset comprises:
 a set of input fluxes representing in part an initial rate of supply in a first set of sub-units representing production and consumption upstream from metabolism; and 
 a set of output fluxes representing in part an initial rate of demand in a second set of sub-units representing production and consumption downstream from metabolism. 
 
     
     
       8. The method of  claim 1 , wherein the initial net demand for the plurality of molecules in the plurality of sub-units representing production and consumption of molecules external to the FBA system is determined by at least one of: a Monte Carlo method, solving a set of ordinary differential equations (ODEs), and solving a set of partial differential equations (PDEs). 
     
     
       9. The method of  claim 1 , wherein:
 the initial state dataset is associated with a first time; 
 the subsequent state dataset is associated with a subsequent time; and 
 the difference between the subsequent solution flux dataset and the initial solution flux dataset represents metabolic production over a time interval between the first time and the subsequent time. 
 
     
     
       10. The method of  claim 1 , further comprising:
 calculating the subsequent solution flux dataset by evaluating the FBA system with the updated objective function limited by the subsequent state dataset until a change in a growth rate of the cell reaches a threshold. 
 
     
     
       11. The method of  claim 10 , wherein the threshold is associated with homeostasis of the cell. 
     
     
       12. A non-transitory computer readable storage medium containing computer program code executable on a processor for causing the processor to perform operations for simulating an outcome of a cell process of at least one cell in a production network, the operations comprising:
 receiving an initial state dataset based on initial net demand for a plurality of molecules in a plurality of sub-units representing production and consumption of molecules external to a flux balance analysis (FBA) system, wherein multiple sub-units of the plurality of sub-units represent transcription, translation, cellular communication, cellular respiration, cellular reproduction, or cellular transport; 
 calculating an initial solution flux dataset by evaluating the FBA system based on a stoichiometric matrix and an objective function, the objective function based on a difference between a first target value for each molecule of the plurality of molecules and a first proportional flux contribution of each molecule of the plurality of molecules, wherein the first target value is included in a set of initial target values calculated based on the initial state dataset; 
 receiving a subsequent net demand for the plurality of molecules from initial solutions to the plurality of sub-units; 
 calculating a subsequent state dataset for the plurality of molecules in the plurality of sub- units based on the initial state dataset, the initial solution flux dataset and the subsequent net demand; 
 updating the objective function, the updated objective function based on a difference between a second target value for each molecule of the plurality of molecules and a second proportional flux contribution of each molecule of the plurality of molecules, wherein the second target value is included in a set of subsequent target values calculated based on the subsequent state dataset; 
 calculating a subsequent solution flux dataset by evaluating the FBA system with the updated objective function; and 
 determining the outcome of the cell process of the at least one cell, the determining includes calculating a difference between the subsequent solution flux dataset and the initial solution flux dataset, wherein the outcome of the cell process corresponds to an estimation of a growth rate of the at least one cell, and wherein an accuracy of the updated objective function is determined based on a comparison of the estimation of the growth rate of the at least one cell to an actual growth rate of the at least one cell. 
 
     
     
       13. The non-transitory computer readable storage medium of  claim 12 , wherein:
 the initial state dataset includes a set of initial molecule concentrations of the plurality of molecules; and 
 the initial net demand for the plurality of molecules comprises: 
 an initial rate of supply in a first sub-unit representing production upstream from metabolism; and 
 an initial rate of demand in a second sub-unit representing consumption downstream from metabolism. 
 
     
     
       14. The non-transitory computer readable storage medium of  claim 13 , wherein the set of initial molecule concentrations of the plurality of molecules comprises:
 a total concentration of each of the plurality of molecules in the plurality of sub-units; and 
 a cushion concentration representing a reserve concentration of each of the plurality of molecules. 
 
     
     
       15. The non-transitory computer readable storage medium of  claim 12 , wherein the initial state dataset further includes:
 a set of intrinsic rate parameters for each of the plurality of molecules, wherein the set of intrinsic rate parameters represents a biological ability of the cell to adjust the subsequent solution flux dataset to the subsequent net demand for the plurality of molecules. 
 
     
     
       16. The non-transitory computer readable storage medium of  claim 15 , wherein the set of intrinsic rate parameters for each of the plurality of molecules includes at least one of: a proportional rate limit, an integral rate limit, and a derivative rate limit. 
     
     
       17. The non-transitory computer readable storage medium of  claim 12 , wherein calculating the initial solution flux dataset by evaluating the FBA system based on the stoichiometric matrix and the objective function limited by the initial state dataset further comprises:
 maximizing the objective function limited by the initial state dataset within a constraint of the stoichiometric matrix to determine a maximum growth rate. 
 
     
     
       18. The non-transitory computer readable storage medium of  claim 12 , wherein the initial solution flux dataset comprises:
 a set of input fluxes representing in part an initial rate of supply in a first set of sub-units representing production and consumption upstream from metabolism; and 
 a set of output fluxes representing in part an initial rate of demand in a second set of sub-units representing production and consumption downstream from metabolism. 
 
     
     
       19. The non-transitory computer readable storage medium of  claim 12 , wherein the initial net demand for the plurality of molecules in the plurality of sub-units representing production and consumption of molecules external to the FBA system is determined by at least one of: a Monte Carlo method, solving a set of ordinary differential equations (ODEs), and solving a set of partial differential equations (PDEs). 
     
     
       20. The non-transitory computer readable storage medium of  claim 12 , wherein:
 the initial state dataset is associated with a first time; 
 the subsequent state dataset is associated with a subsequent time; and 
 the difference between the subsequent solution flux dataset and the initial solution flux dataset represents metabolic production over a time interval between the first time and the subsequent time. 
 
     
     
       21. The non-transitory computer readable storage medium of  claim 12 , further comprising:
 calculating the subsequent solution flux dataset by evaluating the FBA system with the updated objective function limited by the subsequent state dataset until a change in a growth rate of the cell reaches a threshold. 
 
     
     
       22. The non-transitory computer readable storage medium of  claim 21 , wherein the threshold is associated with homeostasis of the cell.